Bottles of Coke and a cream cake from her local bakery were also on the menu when Senator Lambie invited the controversial union boss to a Sunday roast at her Tasmanian home.

She then pleaded with him for four hours to resign.

The unconventional crossbencher followed the home-cooked meal up with another four-hour conversation several weeks later, and believes he's close to standing down.

"I've got him to the point where he'll consider it, so how about he goes one step further and actually carries out the action," Senator Lambie told 3AW Radio on Monday.

"I sweetened him up and all, mate. I still haven't got him over the line yet."

Mr Setka is under mounting pressure to resign as the head of the Victorian construction union, as the Senate prepares to scrutinise draft laws to ban union officials who repeatedly break the law.

Senator Lambie, who holds a crucial swing vote, has declared she will support the union-busting bill if Mr Setka does not stand down.

However, Senator Lambie will try to kill the bill if Mr Setka quits.

"Instead of being such a bloody meathead, he needs to wake up to himself and he needs to resign because he's doing a hell of a lot of damage," she said.

The coalition government has made Mr Setka the public face of its "Ensuring Integrity" bill.

He was convicted of harassing his wife in June and also accused of making disparaging remarks about anti-domestic violence campaigner Rosie Batty.

Opposition Leader Anthony Albanese is determined to expel Mr Setka from the Labor Party, but he has refused.

The government legislation would also make it easier to deregister rogue unions and place restraints on mergers.

It will be scrutinised by a Senate committee later this week, after passing the lower house in July.

The committee is due to report on the bill by late October before it is debated in the upper house.

Deputy opposition leader Richard Marles said the union-busting bill was a distraction from the flagging economy.

"This is legislation which is trying to make the work of trade unions more difficult," he told the ABC.

"When you are thinking about a sluggish economy where wage growth is at the lowest on record, why you would be focused on this beggars belief."

With Labor and the Greens opposed to the legislation, the government needs support from four-out-of-six crossbench senators.

The coalition is confident of securing support for the bill from independent Cory Bernardi and the two One Nation senators, meaning Senator Lambie's vote would make it law.

Centre Alliance's Rex Patrick said he had met with Industrial Relations Minister Christian Porter to discuss removing the power of a minister to initiate action, and raise concerns about overseas convictions being used to deregister an official.

He also wants to see unions and corporations facing the same conduct standards and ensure the good work of unions in supporting workers can continue without disruption.

Australian Associated Press